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x->0
sinx = x-(1/6)x^3 +o(x^3)
sinx/x =1-(1/6)x^2 +o(x^2)
sinx/x-cosx
=1-(1/6)x^2 +o(x^2) -cosx
=(1/2)x^2 -(1/6)x^2 +o(x^2)
=(1/3)x^2 +o(x^2)
//
lim(x->0) (sinx/x-cosx )/x^2
=lim(x->0) (1/3)x^2/x^2
=1/3
sinx = x-(1/6)x^3 +o(x^3)
sinx/x =1-(1/6)x^2 +o(x^2)
sinx/x-cosx
=1-(1/6)x^2 +o(x^2) -cosx
=(1/2)x^2 -(1/6)x^2 +o(x^2)
=(1/3)x^2 +o(x^2)
//
lim(x->0) (sinx/x-cosx )/x^2
=lim(x->0) (1/3)x^2/x^2
=1/3
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